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Finding the Third Proportional to 205,742 and 320,642

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Solution

The third proportional to 205,742 and 320,642 is: 499,709.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,742 : 320,642 = 320,642 : x
  2. Step 2: Convert to fraction form
    205,742/320,642 = 320,642/x
  3. Step 3: Cross multiply
    205,742x = 320,642 × 320,642
  4. Step 4: Simplify right side
    205,742x = 102,811,292,164
  5. Step 5: Solve for x
    x = 102,811,292,164/205,742
  6. Step 6: Final answer
    x = 499,709.79

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.